A study on graceful labeled graph

Abstract

A function defined on a set of vertices of a graph or edges of a newlinegraph or both that assumes labels, mostly integer values, is called a newlinegraph label. A graph whose elements assume a label as defined by the newlinerule of a labeling function is called a labeled graph. Labeling of the newlinegraphs is a center of attraction for many researchers since 1967. It is the newlineyear 1967 in which Rosa introduced three different types of labeling in newlinehis research article. One of the labeling presented by Rosa, the newlineand#120573; and#8722;evaluation was renamed as graceful labeling by Solomon Golomb. newlineIdentifying graphs that accept graceful labeling or constructing graceful newlinegraphs dominated the research in the field of graph theory. In this thesis, newlinea class of graphs that accepts graceful labeling is identified. Further, the newlineapplication of labeled graphs in the field of computer science and newlineformal languages is proposed. The thesis is organized into five chapters. newlineThe problem of discussion and results arrived at is summarised in the newlinefollowing passages. newlineThe first chapter is preparatory. It gives all the concepts required, newlineon which the research investigation is developed. Further, it details the newlinesubsisting results in the related field of research. newlinevii newlineThe graceful labelling of the join of and#119870;1 and shell graph is newlinepresented in the second chapter. newline